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The absence of an energy gap separating valence and conduction bands makesthe low-energy electronic properties of graphene and its multi-layers sensitiveto electron-electron interactions. In bilayers, for instance, interactions arepredicted to open a gap at charge neutrality, turning the system into aninsulator, as observed experimentally. In mono and (Bernal-stacked) trilayers,interactions, although still important, do not have an equally drastic effect,and these systems remain conducting at low temperature. It may be expected thatinteraction effects become weaker for thicker multilayers, whose behaviorshould eventually converge to that of graphite. Here we show that thisexpectation does not correspond to reality by investigating the case ofBernal-stacked tetralayer graphene (4LG). We reveal the occurrence of a robustinsulating state in a narrow range of carrier densities around chargeneutrality, incompatible with the behavior expected from the single-particleband structure. The phenomenology resembles that observed in bilayers, but thestronger conductance suppression makes the insulating state in 4LG visible athigher temperature. To account for our findings, we suggest a naturalgeneralization of the interaction-driven, symmetry-broken states proposed forbilayers. This generalization also explains the systematic even-odd effect ofinteractions in Bernal-stacked layers of different thickness that is emergingfrom experiments, and has implications for the multilayer-to-graphitecrossover.

Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene